Single-axis tomography is a powerful method for three-dimensional (3D) imaging with applications to radiology, other forms of medical imaging, and electron microscopy. The approach is also crucial to the proposed development of X-ray microscopy. The principle draw-back of single-axis tomography is that it requires collecting a large number of views of the object (or patient) under study. This is sever limitation because both X-rays and electrons cause cumulative damage to biological material. In electron microscopy this has meant that the method is only applied to specimens that have been chemically fixed, embedded in plastic, and stained with heavy metals. Such material is can be appreciably altered from its native form. It has been generally assumed that if the illumination level per view is reduced then the 3D image will be too noisy to be useful. Nearly 20 years ago, however, Hegrel and Hoppe pointed out that the illumination level, or dose, required to image a single volume element with statistical significance (i.e. with low enough noise to be detected), could be divided among any number of different views without effecting the quality of the 3D image. In other words the same radiation dose is require to obtain a non-noisy image of a single volume element of the object, wether that dose is used to collect a single, 2D image, or divided among a large number of different views of the object which are then used to compute a 3D image. The theorem was controversial and has been ignored because of a misunderstanding of what is meant by a significant image, and because of unrealistic claims by the authors (in later work) as to what levels of resolution were feasible using single-axis tomography. However, the theorem was never disproved. In the present work we demonstrate the validity of the Hegerl-Hoppe dose fractionation theorem using a computer to simulate image formation. In the extreme case we partitioned the require dose among 18,000 views, each of which had no discernable structure above noise levels, and still obtained the same quality 3D image as when the dose was only fractionated among 90 views (each of which contained a clear 2D image). We also demonstrated that the theorem held for experimentally more realistic conditions, which are too difficult to analyze mathematically, such as a limited angular range for collecting the views, high absorption by the specimen, variable contrast in the specimen, and specimen absorption contributing to the noise. This important theorem tells us that once the required dose is determined it can be fractionated into however many views are required to obtain the 3D image. Our results also show that it is feasible to use single-axis tomography to obtain 3D images of beam labile specimens that have close to native morphology (i.e. frozen hydrated preparations ).